When applying to a PhD, most programs ask for the same or similar requirements. Here are the ones which came up again and again.
1. Transcripts
Pretty much every PhD wants you to already have coursework and a high GPA. If you’ve been a diligent student, you have probably done well for yourself.
A specific note for grading: make sure that if you’re applying to a program, you meet the requirements (especially when applying to programs in different countries).
For an embarrasing example, Oxford asks for you to have a degree with “merit.” I had assumed from some of my other research that it meant that I was fine applying with a 2.1 Honours degree from an Irish university– equavalent to a Magna Cum Laude from a U.S. college. This is not what they meant; the English mean merit as a specific grade award equal to a 1.1 Honours degree or Summa Cum Laude.

2. References
Pretty much everything in higher ed or searching for jobs requires a list of references who can vouch for you, an unknown quantity. Most only ask for two, but one of the ones I applied for asked for three.
If you’re applying for a Ph.D., then you need one of your references to come from your master’s supervisor. That takes care of one.
For your second supervisor, you should ask one of your professors who knew you best, in whose class you excelled, or both. I asked two of my professors since I know I needed three and split the other programs between them.
I talked about asking for references before, but I really should emphasize that you should ask for these as far in advance as possible.
3. A Proposal and/or A Personal Statement
In general, this is the real crux of your application. Essentially, this is where you sell yourself as a candidate and/or talk about the research you want to do and how it fits in at the university.
Between the two, I like the personal statement better. I have some ideas about what I would like to focus on for my Ph.D.– but I have no guarantee that it will be what I and my advisor might land on in the future. More or less, long before you’ll even really get the chance to work on the project, you have to propose it. (There’s a general understanding that your actual disseration is subject to change– but that begs the question about WHY ask me to write it in the first place? As much as I want to be a part of higher academia, these are the kind of problems I find all over the place.) The personal statement is a place where you can talk about you and include research interests (including an idea of what you might want to research). It feels a lot more like I got to show who I am in my personal statement and I feel more comfortable changing my idea because I didn’t have to state my desired disseration as a fact.
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